Actually, it is the freedom of speech clause in the First Amendment that gives fair use rights, as interpreted by the courts. It could even be argued by a future court that the First Amendment invalidates copyright altogether; it wouldn't be the first time a court had changed direction like that.

That is a less extreme change than that from Plessy vs Ferguson to Brown vs the Board of Education, for example. And a good case can be made for freedom of speech trumping copyright; the Constitutional argument for copyright is a practical one for "encouraging" the advance of arts and sciences; eternal copyright has already undercut that argument.